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    General (k, p)-Riemann-Liouville fractional integrals
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Budak, Huseyin
    The main motivation of this study is to establish a general version of the Riemann-Liouville fractional integrals with two exponential parameters k and p which is determined over the (k, p)-gamma function. In particular, we present the harmonic, geometric and arithmetic (k, p)- Riemann-Liouville fractional integrals. When p = k, these integrals reduce to k-Riemann-Liouville fractional integrals. Some formulas relating to general (k, p)-Riemann-Liouville fraction integrals are also given.
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    A GENERALIZATION OF WEIGHTED BILINEAR HARDY INEQUALITY
    (Publishing House of the Romanian Academy, 2021) Benaissa, Bouharket; Zeki Sarıkaya, Mehmet
    In this paper, we give some new generalizations of the weighted bilinear Hardy inequality by using weighted mean operators S:= (Sf)w g, where f nonnegative integrable function with two variables on ? = (0,+?)×(0,+?), defined by with where w is a weight function and g is a nonnegative continuous function on (0,+?). © 2021, Publishing House of the Romanian Academy. All rights reserved.
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    Hermite-Hadamard type inequalities for new conditions on h-convex functions via ? -Hilfer integral operators
    (Springer Basel Ag, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Huseyin
    We employ a new function class called B-function to create a new version of fractional Hermite-Hadamard and trapezoid type inequalities on the right-hand side that involves h-convex and psi -Hilfer operators. We also provide new midpoint-type inequalities using h-convex functions.
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    MORE ON REVERSE OF HOLDER'S INTEGRAL INEQUALITY
    (Kangwon-Kyungki Mathematical Soc, 2020) Benaissa, Bouharket; Budak, Huseyin
    In 2012, Sulaiman [7] proved integral inequalities concerning reverse of Holder's. In this paper two results are given. First one is further improvement of the reverse Holder inequality. We note that many existing inequalities related to the Holder inequality can be proved via obtained this inequality in here. The second is further generalization of Sulaiman's integral inequalities concerning reverses of Holder's [7].
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    On some Grüss-type inequalities via k-weighted fractional operators
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarikaya, Mehmet Zeki
    In this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr & uuml;ss-type fractional integral inequalities. Furthermore, we establish and provide proofs for a set of inequalities that incorporate k-weighted fractional integrals.
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    On some new Hardy-type inequalities
    (Wiley, 2020) Benaissa, Bouharket; Sarikaya, Mehmet Zeki; Senouci, Abdelkader
    In this paper, we give some new types of the classical Hardy integral inequality by including a second parameter q and using weighted mean operators S-1 := (S-1)(g)(w) and S-2 := (S-2)(g)(w) defined by S-1(x) = 1/W(x) integral(x)(a) w(t)g(f(t))dt, S-2(x) = integral(x)(a) w(t)/W(t)g(f(t))dt, with W(x) = integral(x)(0) w(t)dt, for x is an element of(0,+infinity), where w is a weight function and g is a real continuous function on (0,+infinity).
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    On the refinements of some important inequalities with a finite set of positive numbers
    (Wiley, 2024) Benaissa, Bouharket; Sarikaya, Mehmet Zeki
    In this research, a novel method for enhancing the Holder-Iscan inequality through the utilization of both integrals and sums, as well as the mean power inequality, has been introduced. This approach outperforms traditional Holder and mean power integral inequalities by employing a finite set of functions. Through the careful selection of the function phi$$ \phi $$, an entirely new category of classical inequalities emerges for both Holder and mean power inequalities.
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    Some Hardy-type integral inequalities involving functions of two independent variables
    (Springer, 2021) Benaissa, Bouharket; Sarikaya, Mehmet Zeki
    In this paper, we give some new generalizations to the Hardy-type integral inequalities for functions of two variables by using weighted mean operatorsS(1) := S1(w) f and S-2 := S-2(w) f defined by S-1(x, y) = 1/W(x)W(y) integral(x)(x/2) integral(y)(y/2) w(t)w(s) f (t, s)dsdt, and S-2(x, y) = integral(x)(x/2) integral(y)(y/2) w(t)w(s)/W(t)W(s) f (t, s)dsdt, with W (z) = integral(z)(0) w(r)dr f or z is an element of (0,+infinity), where w is a weight function.
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    Weighted fractional inequalities for new conditions on h-convex functions
    (Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Huseyin
    We use a new function class called B-function to establish a novel version of Hermite-Hadamard inequality for weighted psi-Hilfer operators. Additionally, we prove two new identities involving weighted psi-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h.